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- [[Mathematics of Computation]] ([[MOC]]) is [[Scientific journal]] dedicated to numerical analysis, computational discrete mathematics, number theory, algebra, combinatorics, and related fields.2 KB (344 words) - 07:02, 1 December 2018
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- <b>Logic</b> is part of mathematics that deals with Boolean algebra. This algebra deals with logical variables. Creation of logics is usually attributed to [[George Bool]]8 KB (1,403 words) - 14:24, 20 June 2013
- is the \(\mathbb C \mapsto \mathbb C\) function, which is solution of equations ...n]] of [[exponential]] to base \(b\). Exponential is [[transfer function]] of tetration.21 KB (3,175 words) - 23:37, 2 May 2021
- ...space to itself or to another space, and also the graphical representation of such a function. Such a representation is called '''map'''. ...surface of the Earth (or that of another planet) is mapped to the surface of14 KB (2,275 words) - 18:25, 30 July 2019
- [[Superfunction]] comes from iteration of some function. ...derbrace{T\Big(T\big(... T(t)...\big)\Big)}} \atop {z \mathrm{~evaluations~of~function~}T\!25 KB (3,622 words) - 08:35, 3 May 2021
- [[Natural pentation]] is [[supefrunction]] of [[natural tetration]] tet; [[natural pentation]] satisfies the [[transfer e ...atural tetration]], which is solution \(L=L_0\approx -1.8503545290271812\) of equation \(\mathrm{tet}(L)=L\).7 KB (1,090 words) - 18:49, 30 July 2019
- [[Place of Science in the Human Knowledge]] ([[Place of science in the human knowledge]])100 KB (14,715 words) - 16:21, 31 October 2021
- ..." style="float:right;width:246px"><div style="width:260px"><small>Examples of things considered as [[science]]:</small> [[Complex map]] of function [[AuSin]]</small> !-->111 KB (2,581 words) - 16:54, 17 June 2020
- ...l]] (half-iteration of [[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\). ...=\mathrm{Factorial}\). It is assumed that \(z\!=\!2\) is [[regular point]] of \(\sqrt{!\,}(z)\), and13 KB (1,766 words) - 18:43, 30 July 2019
- Terras, R. "On the Existence of a Density." Acta Arith. 35, 101-102, 1979. is subsequence of the [[Collatz sequense]]5 KB (798 words) - 18:25, 30 July 2019
- A [[fractional iterate]] $\phi$ of an analytic function $f$ at fixpoint $a$ is called regular, iff $\phi$ is a ...ait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.20 KB (3,010 words) - 18:11, 11 June 2022
- '''SuperFactorial''', or "superfactorial" is [[superfunction]] of [[factorial]] constructed at its [[fixed point]] 2. Here, the upper index of a function indicates the number of [[iteration]]s.18 KB (2,278 words) - 00:03, 29 February 2024
- ...er function]] \(T\), the '''Abel function''' \(G\) is [[inverse function]] of the corresponding [[superfunction]] \(F\), id est, \(G=F^{-1}\). In certain range of values of \(z\), this equation is equivalent of the [[Transfer equation]]4 KB (547 words) - 23:16, 24 August 2020
- [[File:KellerDoyaT.png|300px|thumb|Transfer functions of laser amplifiers with simple kinetics for the short pulses ([[Keller functi ...ion of the state of the system in terms of its state at the precedent step of evolution.11 KB (1,644 words) - 06:33, 20 July 2020
- [[File:Japan.gif|320px]] Map of Japan by [[CZ]]<ref name="CZpic">http://en.citizendium.org/wiki/Japan</ref> ...日本 , にほん) is country in the Pacific Ocean, near the East side of Asia,15 KB (2,106 words) - 13:37, 5 December 2020
- [[ArcTetration]] \( \mathrm{ate} \) is inverse function of [[tetration]] .... Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation 78 (2009), 1647-1670.7 KB (1,091 words) - 23:03, 30 November 2019
- [[File:Tet5loplot.jpg|400px|thumb|Graphical search for the [[fixed point]]s of [[tetration]]; \(y\!=\!\mathrm{tet}_b(x)\) versus \(x\) for various \(b\) ] For a given function \(f\), the '''fixed point''' is solution \(L\) of equation4 KB (574 words) - 18:26, 30 July 2019
- ...upports this language, developed by the [[Wolfram corporation]] in the end of century 20 for ...ation of functions, plotting graphics and other things that require some [[mathematics]].12 KB (1,901 words) - 18:43, 30 July 2019
- The [[Doya function]] and its iterates appear as the [[transfer function]] of an [[optical amplifier]] with simplest kinetic model. In vicinity of the real axis (While \(|\Im(z)| \!<\! \pi\)), the [[Doya function]] can be19 KB (2,778 words) - 10:05, 1 May 2021
- ...nction \(T\), called [[transfer function]], the holomorphic solution \(F\) of [[Transfer equation]] In any pair of holomorphic functions \(F\), \(G\!=\!F^{-1}\),11 KB (1,565 words) - 18:26, 30 July 2019
- ...root of exponential]] \(\varphi=\sqrt{\exp}=\exp^{1/2}\) is half-iteration of the [[exponential]], id est, such function that its second iteration gives ...rphi\) is assumed to be [[holomorphic function]] for some domain of values of \(z\).5 KB (750 words) - 18:25, 30 July 2019
- [[File:PowIteT.jpg|400px|thumb|Fig.1. Iterates of \(T(z)=z^2~\): \(~y\!=\!T^n(x)\!=\!x^{2^n}~\) for various \(n\)]] [[File:FacIteT.jpg|400px|thumb|Fig.2. Iterates of [[Factorial]]: \(~y\!=\!\mathrm{Factorial~}^{~n}(x)~\) for various \(n\)]14 KB (2,203 words) - 06:36, 20 July 2020
- ...usually referring to [[mathematics]], that is proved baser on certain set of axioms. For example, the existence and uniqueness of the holomorphic [[tetration]] with certain properties is declared as theore2 KB (248 words) - 14:33, 20 June 2013
- ...\) is assumed; the tetration approaches the fixed points \(L\) and \(L\)^* of exponential. Existence of natural tetration been indicated in 1950 by [[Hellmuth Kneser]] in 195014 KB (1,972 words) - 02:22, 27 June 2020
- ...нглийской версии этой статьи, см. [[Square root of factorial]].6 KB (312 words) - 18:33, 30 July 2019
- Корень из факториала ([[square root of factorial]]) – это такая функция \(h\), что ...amlib.ru/img/g/garik/dubinushka/index.shtml Logo of the Physics Department of the Moscow State University. (In Russian);7 KB (381 words) - 18:38, 30 July 2019
- [[File:Filogbigmap100.png|400px|right|thumb|[[Complex map]] of Filog; \(u\!+\! \mathrm i v=\mathrm{Filog}(x\!+\! \mathrm i y)\) ]] ...t|thumb|\(u\!+\! \mathrm i v=\mathrm{Filog}(x\!+\! \mathrm i y)\), zoom in of the central part ]]4 KB (572 words) - 20:10, 11 August 2020
- [[File:Shelre60.png|500px]]<small> Explicit plot of real and imaginary parts of tetration to base \(b\!=\!s\)</small> [[File:Shelima600.png|500px]]<small>Distribution of tetration to \(b\!=\!s\) along the imaginary axis</small>5 KB (707 words) - 21:33, 13 July 2020
- '''GLxw2048.inc''' is text file, containing nodes and weights of the ...update to another number of points is straightforward. For moderate number of nodes (maximum 32), the108 KB (1,626 words) - 18:46, 30 July 2019
- '''Iterated Cauchi''' is algorithm of iterative solution of the [[Transfer equation]] \(U=T^{-1}\) is also holomorphic in the working range of valies.6 KB (987 words) - 10:20, 20 July 2020
- '''WARNING!''' The formulas of this article are not yet verified with pics, In publications, it is difficult to see difference between meanings of terms '''Hankel transform''' and '''Bessel transform''' is found. In TORI,8 KB (1,183 words) - 10:21, 20 July 2020
- // [[F45E.cin]] is routine for evaluation of the [[superfunction]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed po ...ait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, v.271, July 2010, p.1727-1756.1 KB (139 words) - 18:48, 30 July 2019
- // [[F45E.cin]] is routine for evaluation of the [[Abel function]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed po ...ait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, v.271, July 2010, p.1727-1756.2 KB (163 words) - 18:47, 30 July 2019
- One of the inverse function of [[ArcLambertW]] is called [[LambertW]] In wide ranges of values of \(z\), the relations3 KB (499 words) - 18:25, 30 July 2019
- [[SuZex]] is [[superfunction]] of [[ArcLambertW]], denoted also as [[zex]], \(\mathrm{zex}(z)=z \exp(z)\). The [[explicit plot]] of function [[SuZex]] is shown in Figure 1 in comparison with that function [[7 KB (1,076 words) - 18:25, 30 July 2019
- [[File:AuZexLamPlotT.jpg|620px|thumb|Fig.1. Plot of [[AuZex]] (thick curve) in comparison to [[LambertW]] (thin curve) ]] [[Auzex]] is inverse function of [[SuZex]]; \(\mathrm{AuZex} = \mathrm{SuZex}^{-1}\)6 KB (899 words) - 18:44, 30 July 2019
- at least in some vicinity of zero, and \(~K\!=\!T'(0)~\). Function \(~f~\) is requested to built-up. ...scribes the variation of value of function \(~f~\) at the scaling, zooming of its argument with factor \(~K~\).10 KB (1,627 words) - 18:26, 30 July 2019
- ...e [[complex map]]s of [[tetration]] \(\mathrm{tet}_b\) to different values of base \(b\). For real values of base \(b\), the real-real plots \(y\!=\!\mathrm{tet}_b(x)\) are shown in th5 KB (761 words) - 12:00, 21 July 2020
- ...2009). Solutions of F(z+1)=exp(F(z)) in the complex plane.. Mathematics of Computation, 78: 1647-1670. While Russian version of that article, id est, [[Тетрация]] is not loaded, the English vers16 KB (821 words) - 14:42, 21 July 2020
- ...function \(f(z)=\exp^n(z)\), where upper superscript indicates the number of iteration. ...the number in superscript after a name of any function denotes the number of iteration. This notation is neither new, nor original;7 KB (1,161 words) - 18:43, 30 July 2019
- [[Iterate_of_linear_fraction]] (or [[iteration of linnet friaction]]) refers to function [[Iterate]] of a [[linear fraction]] can be expressed with also some linear fraction. This13 KB (2,088 words) - 06:43, 20 July 2020
- ...of [[abelfunction]]s, [[superfunction]]s, and the non-integer [[iterate]]s of holomorphic functions. In particular, results for [[tetration]], [[arctetration]] and [[iterate]]s of [[exponential]] are presented.15 KB (2,166 words) - 20:33, 16 July 2023
- ...at used in the [[Computability theory]]. While no commonly accepted system of notations is established, at the reference to the Ackermann function, eithe ...ontent of this article is published in 2014 at [[Applied and Computational Mathematics]]10 KB (1,534 words) - 06:44, 20 July 2020
- ..., that provides approximation of [[natural tetration]] for moderate values of the argument. // This fit had been used to guess the asymptotic behaviour of [[tetration]] at \(\mathrm i \infty\).1 KB (253 words) - 18:48, 30 July 2019
- [[Applied and Computational Mathematics]] is [[scientific journal]] dedicated to development of mathematical principles and practical issues in computational mathematics.1 KB (134 words) - 06:58, 1 December 2018
- [[File:Expe1emapT1000.jpg|200px|thumb|[[Complex map|Map]] of \(~f\!=\!\eta\!=\!\exp_{\exp(1/\mathrm e)}~\); here \(~u+\mathrm i v=f(x\!+ [[File:Loge1emapT1000.jpg|200px|thumb|[[Complex map|Map]] of \(~f\!=\!\log_{\exp(1/\mathrm e)}~\); here \(~u+\mathrm i v=f(x\!+\!\mathrm4 KB (559 words) - 17:10, 10 August 2020
- http://en.wikipedia.org/wiki/File:Boy_on_snow_sled,_1945.jpg Father of JGKlein. Boy on snow sled, 1945. ...n of sin is expressed with sinˆn(z)=SuSin(n+AuSin(z)), where the number n of iteration has no need to be integer. ..7 KB (1,031 words) - 03:16, 12 May 2021
- ...[Regular iteration]] is not possible: in the leading term of the expansion of superfunction with exponentials, the increment \(k\!=\!\ln(T'(L)\) becomes However, even if the \(T'(L)\!=\!1\), construction of superfunction is possible. Few examples are considered in this article.11 KB (1,715 words) - 18:44, 30 July 2019
- [[Mathematics of Computation]] ([[MOC]]) is [[Scientific journal]] dedicated to numerical analysis, computational discrete mathematics, number theory, algebra, combinatorics, and related fields.2 KB (344 words) - 07:02, 1 December 2018
- [[Pentation]] is specific [[superfunction]] of [[tetration]], constructed with [[regular iteration]] at its lowest real fi if the base of tetration is \(\mathrm e=\exp(1)\approx 2.71\), then the tetration is calle5 KB (803 words) - 18:48, 30 July 2019
- ...jmp.pdf D.Kouznetsov. TORI axioms and the applications in physics. Journal of Modern Physics, 2013, v.4, p.1151-1156. ...76.htm D.Kouznetsov. Support of non-traditional concepts. Far East Journal of Mechanical Engineering and Physics, 1, No.1, p.1-6 (2010)6 KB (950 words) - 18:48, 30 July 2019
